Optimal. Leaf size=10 \[ -\frac {1}{2 d x^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 30}
\begin {gather*} -\frac {1}{2 d x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{d x^3} \, dx &=\frac {\int \frac {1}{x^3} \, dx}{d}\\ &=-\frac {1}{2 d x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} -\frac {1}{2 d x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 9, normalized size = 0.90
method | result | size |
gosper | \(-\frac {1}{2 d \,x^{2}}\) | \(9\) |
default | \(-\frac {1}{2 d \,x^{2}}\) | \(9\) |
norman | \(-\frac {1}{2 d \,x^{2}}\) | \(9\) |
risch | \(-\frac {1}{2 d \,x^{2}}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 8, normalized size = 0.80 \begin {gather*} - \frac {1}{2 d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.74, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2 \, d x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 8, normalized size = 0.80 \begin {gather*} -\frac {1}{2\,d\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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